Analysis of an elastodynamic contact problem by applying the boundary element method. (An approach using the penalty function method)

A boundary element technique for elastodynamic contact problems is suggested by using the penalty function method. We consider an impingement between two elastic bodies which must satisfy contact conditions of the displacements and tractions on the interface boundary corresponding to contact states such as open, sticking and slipping states. A functional of the virtual work is adopted and the contact conditions at each time step are assembled in the functional by using the penalty function method. An integral representation which provides the displacement field at each time step in terms of boundary values of displacements and tractions is derived with the aid of the method of weighted residuals. This formulation does not need to expand or decompose coefficient matrices in a final system of algebraic equations to satisfy the contact conditions. Results of impinging problems between long bars and between circular disks are also described.